Australia on Sunday agreed to help the United States in an international effort to transport weapons to Kurdish forces fighting the IS in northern Iraq, as well as humanitarian air drops to the besieged town of Amerli.

But with newspapers reporting that elite SAS soldiers will fly with the crews ferrying arms and munitions as protection and could be stationed on the ground if Australia joins an air strike campaign, there were demands for Abbott to explain his strategy.

“Everybody believes that we are simply running behind President (Barack) Obama who himself last week said he has not got a strategy,” said Greens Party leader Christine Milne.

Independent MP Andrew Wilkie said it was “insane” that the power to approve military action rested with Abbott and his senior ministers and demanded any decisions be debated in parliament.

The government’s decision to help arm the Kurdish peshmerga has the support of the Labor opposition and in a statement to parliament Abbott acknowledged people were apprehensive about getting involved in another conflict.

But he defended joining allies including the US, Britain and France, with US Secretary of State John Kerry calling for a global coalition to combat IS and its “genocidal agenda”.

“I refuse to call this hideous movement ‘Islamic State’ because it’s not a state; it is a death cult,” added the prime minister.

“In good conscience, Australia cannot leave the Iraqi people to face this horror, this pure evil, alone or ask others to do in the name of human decency what we won’t do ourselves.

“It is right to do what we prudently and proportionately can to alleviate this suffering, to prevent its spread and to deal with its perpetrators.”

Abbott said that so far there had been no request from Iraq or the United States to take part in further military action but any call for more help would be considered.

“Should such a request come from the Obama administration and supported by the government of Iraq, it would be considered against these criteria: is there a clear and achievable overall objective?,” he said.

“Is there a clear and proportionate role for Australian forces? Have all the risks been properly assessed? And is there an overall humanitarian objective in accordance with Australia’s national interests?”

IS has prompted widespread concern as it advances in both Syria and Iraq, killing hundreds of people, including in gruesome beheadings and mass executions.

The US began air strikes against the group in Iraq last month, but has yet to decide if it will do the same in Syria.